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Minimizing Delays in the GI / G /1 Queue

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  • Ward Whitt

    (AT&T Bell Laboratories, Holmdel, New Jersey)

Abstract

What service-time distribution minimizes delays in a GI / G /1 queue with given renewal arrival process and given mean service time? It is natural to conjecture that the deterministic service-time distribution with unit mass on the mean is optimal for all objective functions of the form Ef ( W ) where f is a nondecreasing function of the steady-state delay W . However, we show that this conjecture is false. In fact, for hyperexponential interarrival-time distributions (mixtures of two exponential distributions), the service-time distribution minimizing the average delay maximizes the proportion of customers delayed.

Suggested Citation

  • Ward Whitt, 1984. "Minimizing Delays in the GI / G /1 Queue," Operations Research, INFORMS, vol. 32(1), pages 41-51, February.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:1:p:41-51
    DOI: 10.1287/opre.32.1.41
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    696 minimizing delays;

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